An extended TODIM approach with intuitionistic linguistic numbers

• Author: Jian‐qiang Wang,Jing Wang,Su‐min Yu
• Date: 01 May 2018
• DOI: http://doi.org/10.1111/itor.12363
• Published date: 01 May 2018

Intl. Trans. in Op. Res. 25 (2018) 781–805

DOI: 10.1111/itor.12363

INTERNATIONAL

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IN OPERATIONAL

RESEARCH

An extended TODIM approach with intuitionistic

linguistic numbers

Su-min Yu, Jing Wang and Jian-qiang Wang

School of Business, Central South University, Changsha 410083, P.R. China

E-mail: 151601018@csu.edu.cn [Yu]; wangjingcsuft@csu.edu.cn [Jing Wang];jqwang@csu.edu.cn [Jian-qiang Wang]

Received 23 June2016; received in revised form 28 September 2016; accepted 10 October 2016

Abstract

In many practical problems, multiple alternatives are ranked with respect to related criteria, and the criteria’s

weights are usually unknown. In order to solvethis kind of multicriteria decision making (MCDM) problem,

this paper proposes an interactive MCDM approach based on an acronym in Portuguese of interactive

and multicriteria decision-making (TODIM) method and nonlinear programming (NLP) with intuitionistic

linguistic numbers (ILNs). First, by comparing the existing operations and comparison methods for ILNs,

new operations and a new comparison method are defined based on linguistic scale functions to obtain

rational results.Second, considering their linguistic ter ms, membership degrees, and nonmembership degrees

as a whole, the generalized distance between ILNs is defined with an adjustable parameter. Third, the total

ranking of alternativesis obtained using the proposed NLP-based TODIM approach based on the generalized

ILN distance. Finally, an example of selecting hotels from a tourism website is presented to verify the

validity and feasibility of the proposed approach.A comparison with existing methods is also conducted and

analyzed.

Keywords:intuitionistic linguistic numbers; TODIM; nonlinear programming; generalized distance function

1. Introduction

As society rapidly develops, the factors that people should consider in decision-making problems

continue to increase. As a result, multicriteria decision-making (MCDM) problems have become

an important focus of research in recent years (Ilgin et al., 2015; Gul et al., 2016; Peng et al.,

2016). In situations with incomplete information in uncertain environments, crisp numbers cannot

meet the requirements of describing alternatives with respect to different criteria. In order to

evaluate alternatives accurately, Zadeh (1965) proposed fuzzy sets (FSs), which are characterized

by a membership degree; subsequently, numerous methods have been proposed based on FSs to

deal with various MCDM problems (Yager, 1977; Chen, 2000; Wang et al., 2016b). However, some

researchers hold the view thatthe single membership degree of an FS is inadequate when considering

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782 S.-M. Yu et al. / Intl. Trans.in Op. Res. 25 (2018) 781–805

nonmembership degrees would contribute valuable information. Based on that idea, Atanassov

(1986, 1989) proposed intuitionistic FSs (IFSs), which are characterized by both membership

degrees and nonmembership degrees; IFSs are a generalization of the FS concept. Since then,

interval-valued IFSs (Atanassov and Gargov, 1989; Wu et al., 2013; Cao et al., 2016), intuitionistic

triangular fuzzy numbers (Shu et al., 2006; Wang and Zhang, 2009), and triangular intuitionistic

fuzzy numbers (Zhang and Liu, 2010; Ye, 2012) have been defined and researched as extensions of

IFSs in order to address MCDM problems (Borana et al., 2009; Zhang and Liu, 2011; Tian et al.,

2015; Nan et al., 2016). Furthermore, Wang and Li (2010) proposed intuitionistic linguistic sets

(ILSs) that consider the convenience of linguistic variables and the comprehensiveness of IFSs in

assessing alternatives.

Since Wang and Li (2010) proposed ILSs, a number of research studies (Liu, 2013; Liu and

Wang, 2014; Su et al., 2014; Wang et al., 2014b, 2015) have been conducted based on the concept.

Because intuitionistic linguistic numbers (ILNs) are the predominant carriers of information in

ILSs, many applications of ILSs are based on ILNs. Liu (2013) defined an intuitionistic linguis-

tic power generalized weighted average operator and an intuitionistic linguistic power generalized

ordered weighted average operator, using the operators to propose two corresponding MCDM

methods. Su et al. (2014) proposed a new method using the quasi-arithmetic Atanassov’s intu-

itionistic linguistic ordered weighted averaging distance (Quasi-AILOWAD) operator. Wang et al.

(2014b, 2015) defined the intuitionistic linguistic ordered weighted averaging operator, intuitionistic

linguistic hybrid aggregation operator, intuitionistic linguistic ordered weighted geometric opera-

tor, and intuitionistic linguistic hybrid geometric operator; they then proposed MCDM methods

based on the different operators in which criteria values are ILNs and the criteria weight in-

formation is completely known. As methods based on ILNs have proliferated, researchers have

explored many potential applications of ILNs. However, all of the methods described above are

based on the aggregation operator, such that the differences of alternatives under different cri-

teria are lost. Furthermore, the operations and comparison methods for ILNs are unreasonable

because their linguistic terms, membership degrees, and nonmembership degrees are separated

to calculate results. Therefore, given the validity of ILNs in expressing information, additional

research should explore rational operations, comparison methods, and MCDM methods with

ILNs.

In general, when it comes to considering the behavior of decision makers, an acronym in Por-

tuguese of interactive and multicriteria decision-making (TODIM) method (Gomes and Lima,

1992), which was proposed by Gomes and Lima based on the prospect theory, would be the prefer-

able method comparing with another methods (Gomes and Gonz´

alez, 2012; Gomes et al., 2013;

Tan et al., 2015; Zhou et al., 2016). Later, Gomes and Rangel (2009) defined a reference value

for the rents of these properties using the TODIM method of multicriteria decision aiding. Zhang

and Xu (2014) extended the TODIM method in order to consider the decision maker’s psycho-

logical behavior in hesitant fuzzy environments. Krohling et al. (2013) developed an intuitionistic

fuzzy TODIM method, which accounts for uncertainty modeled by intuitionistic trapezoidal fuzzy

numbers in the decision matrix. Lourenzutti and Krohling (2013) proposed a generalization of the

TODIM method that considers both intuitionistic fuzzy information and an underlying random

vector that affects the performance of the alternatives. Ji et al. (2016) proposed a projection-based

TODIM method for multivalued neutrosophic environments and applied it to personnel selection.

Wang et al. (2016a) proposed a likelihood function for multihesitant fuzzy linguistic term elements,

C

2016 The Authors.

International Transactionsin Operational Research C

2016 International Federation of OperationalResearch Societies